Lesson 22

The purpose of this warm-up is to elicit the idea that designs are built from many smaller shapes, which will be useful when students construct their own designs in a later activity. While students may notice and wonder many things about these images, perpendicular lines, parallel lines, and shapes that they know how to construct are the important discussion points. This prompt gives students opportunities to see and make use of structure (MP7). The specific structures they might notice are perpendicular lines and other shapes from constructions they have performed throughout the section.

Display the image for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice with their partner, followed by a whole-class discussion.

Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information. If hexagons do not come up during the conversation, ask students to discuss where they see a hexagon.

Students begin by examining a design. Next, they work to recreate it and record instructions for another student to make it as they work. This provides opportunities for students to practice their construction techniques while identifying geometric figures and their properties.

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).

Distribute copies of the blackline master. Give students access to blank paper on which to create their designs. 

If students have access to dynamic geometry software, suggest that GeoGebra Geometry from Math Tools might be helpful in this activity.

For students who are having trouble getting started, consider pointing them toward the display of construction techniques. Tell these students that each pattern starts with a regular hexagon or a triangle, and from there, they can use diagonals to find different points of intersection around which to center circles.

Invite a few students to share their design and explain what constructions they used to make it.

This activity invites students to use what they have learned about constructions to create their own design. It is not required for students to begin from the construction of a regular hexagon, but it might be a good starting point for students who have trouble starting.

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).

If students are unsure where to start, suggest they review all the constructions they have done so far for inspiration.

If students will not be completing the Make Their Design activity: Invite a few students to share their design and explain what constructions they used to make it.

Students have the opportunity to practice constructing, identifying congruent parts, and justifying their thinking by following the instructions for another student's design.

Invite students to trade instructions with someone who is not their partner while keeping the design secret.

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).

Ask students to compare their design with the person they received the instructions from.

Invite students to share what made instructions easier or harder to follow. (It's easier when each step is written out and there are labels to help orient me. It's harder when all the steps are together in one long list without labels or stopping points.)